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Tohoku Mathematical Journal
SECOND SERIES VOL. 61, NO. 1
|Tohoku Math. J.|
61 (2009), 1-40
COMPLETE CLASSIFICATION OF PARALLEL SURFACES IN 4-DIMENSIONAL LORENTZIAN SPACE FORMS
Bang-Yen Chen and Joeri Van der Veken
(Received November 19, 2007, revised June 13, 2008)
In this paper we completely classify parallel non-degenerate surfaces in 4-dimensional Lorentzian space forms. In addition, we also completely classify non-degenerate surfaces with parallel mean curvature vector in 4-dimensional Lorentzian space forms.
2000 Mathematics Subject Classification.
Primary 53B25; Secondary 53C50, 83C15.
Key words and phrases.
Lorentzian space form, parallel second fundamental form, surface with parallel mean curvature vector, parallel surface.
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